Removed O(n^2) time and space overhead from Monte Carlo EQI at the cost of making each trial O(n) time

Author: ThomasOldham

lib/eqi/MonteCarloEqi.go

@@ -8,6 +8,11 @@ import (
 	"strconv"
 )
 
+type gadgetIndexer struct {
+	sequence types.GadgetId
+	addressIndex int
+}
+
 func MonteCarloEqi(f1 types.Fingerprint, f2 types.Fingerprint, form url.Values) (float64, error) {
 	min, err := strconv.ParseInt(form.Get("min"), 0, 64)
 	if err != nil {
@@ -22,31 +27,59 @@ func MonteCarloEqi(f1 types.Fingerprint, f2 types.Fingerprint, form url.Values)
 		return 0, errors.New("Could not parse number of trials.")
 	}
 
-	offsets := offsetSets(f1, f2)
+	gis := gadgetIndexers(f1)
 
 	sum := 0
 	for i := 0; i < int(trials); i++ {
-		if monteCarloTrial(offsets, min, max) {
+		if monteCarloTrial(f1, f2, gis, min, max) {
 			sum++
 		}
 	}
 	return float64(sum) / float64(trials), nil
 }
 
-func monteCarloTrial(displacements []map[types.Offset]bool, minGadgets, maxGadgets int64) bool {
+func monteCarloTrial(f1, f2 types.Fingerprint, gadgetIndexers []gadgetIndexer, minGadgets, maxGadgets int64) bool {
 	numGadgets := minGadgets
 	if maxGadgets > minGadgets {
 		numGadgets += rand.Int63n(maxGadgets - minGadgets)
 	}
 
-	workingOffsetSet := offsetSetCopy(randomGadgetDisplacementSet(displacements))
+	workingOffsetSet := offsetSetCopy(randomGadgetDisplacementSet(f1, f2, gadgetIndexers))
 	for i := int64(1); i < numGadgets && len(workingOffsetSet) > 0; i++ {
-		gadgetOffsetSet := randomGadgetDisplacementSet(displacements)
+		gadgetOffsetSet := randomGadgetDisplacementSet(f1, f2, gadgetIndexers)
 		offsetSetAndEqual(&workingOffsetSet, &gadgetOffsetSet)
 	}
 	return len(workingOffsetSet) > 0
 }
 
+func randomGadgetDisplacementSet(f1, f2 types.Fingerprint, gadgetIndexers []gadgetIndexer) map[types.Offset]bool {
+	index := rand.Intn(len(gadgetIndexers))
+	return offsetSetByIndex(f1, f2, gadgetIndexers[index])
+}
+
+func gadgetIndexers(f types.Fingerprint) []gadgetIndexer {
+	var indexers []gadgetIndexer
+	for sequence, addresses := range f {
+		for i := range addresses {
+			indexers = append(indexers, gadgetIndexer {
+				sequence:   sequence,
+				addressIndex:  i,
+			})
+		}
+	}
+	return indexers
+}
+
+func offsetSetByIndex(f1, f2 types.Fingerprint, gi gadgetIndexer) map[types.Offset]bool {
+	oldAddress := f1[gi.sequence][gi.addressIndex]
+	newAddresses := f2[gi.sequence]
+	offsets := make([]types.Offset, len(newAddresses), len(newAddresses))
+	for i := 0; i < len(newAddresses); i++ {
+		offsets[i] = types.Offset(newAddresses[i] - oldAddress)
+	}
+	return offsetSet(offsets)
+}
+
 func offsetSet(values []types.Offset) map[types.Offset]bool {
 	ret := map[types.Offset]bool{}
 	for i := 0; i < len(values); i++ {
@@ -69,25 +102,4 @@ func offsetSetCopy(s map[types.Offset]bool) map[types.Offset]bool {
 		ret[key] = value
 	}
 	return ret
-}
-
-func offsetSets(f1, f2 types.Fingerprint) []map[types.Offset]bool {
-	ret := make([]map[types.Offset]bool, 0)
-	for gadget, addresses := range f1 {
-		for i := 0; i < len(addresses); i++ {
-			oldAddress := addresses[i]
-			newAddresses := f2[gadget]
-			offsets := make([]types.Offset, len(newAddresses), len(newAddresses))
-			for i := 0; i < len(newAddresses); i++ {
-				offsets[i] = types.Offset(newAddresses[i] - oldAddress)
-			}
-			ret = append(ret, offsetSet(offsets))
-		}
-	}
-	return ret
-}
-
-func randomGadgetDisplacementSet(displacements []map[types.Offset]bool) map[types.Offset]bool {
-	index := rand.Intn(len(displacements))
-	return displacements[index]
 }

lib/eqi/OffsetsIntersectionEqi.go

@@ -48,4 +48,20 @@ func successfulAttacks(chosenIndices []int, offsets []map[types.Offset]bool, len
 		sum += successfulAttacks(append(chosenIndices, i), offsets, length)
 	}
 	return sum
+}
+
+func offsetSets(f1, f2 types.Fingerprint) []map[types.Offset]bool {
+	ret := make([]map[types.Offset]bool, 0)
+	for gadget, addresses := range f1 {
+		for i := 0; i < len(addresses); i++ {
+			oldAddress := addresses[i]
+			newAddresses := f2[gadget]
+			offsets := make([]types.Offset, len(newAddresses), len(newAddresses))
+			for i := 0; i < len(newAddresses); i++ {
+				offsets[i] = types.Offset(newAddresses[i] - oldAddress)
+			}
+			ret = append(ret, offsetSet(offsets))
+		}
+	}
+	return ret
 }